Canada was established as the country in 1867, so no he's Canadian. (I know it was still a British colony, however, politically, anyone born after confederation in Canada is considered a Canadian citizen.)

I'm not sure if Americans actually had the "You have to be born American to be president" law at the time. But in any case I suppose that's true. I just figured that Logan would be born to British Subjects and taught his original roots, so he would consider himself more British than anything (not to mention fighting for Britain during the World Wars)